(Shall I use the binomial distribution to compute?)

Given a bin with n balls, n of which are Blue and the rest are Red (where > 0 is some real number).

Start removing balls at random (no replacements) until the bin is empty. In each time-step, if the ball removed is Blue, you earn 5 dollars and otherwise you lose 5 dollars. Define the random variable X as the total amount of money that you earn (or lose) at the end of the game.

(1).Suppose E[X] = 100 and n = 1000. What is ?

(2). Suppose that =12 and n= 100,000.Calculate Var(X).

(3).Will the variance become larger or smaller if we stop the game after we remove exactly (n/2 )balls?Explain your reasoning in words (no need to compute the variance).